The Crossing Statistic: Beyond Chi Square Analysis

Arman Shafieloo (Oxford University)

Abstract:
We propose a new statistic that has been designed to be used in situations where the intrinsic dispersion of a data set is not well known: `The Crossing Statistic'. This statistic is in general less sensitive than `chi^2' to the intrinsic dispersion of the data, and hence allows us to make progress in distinguishing between different models using goodness of fit to the data even when the errors involved are poorly understood. The proposed statistic makes use of the shape and trends of a model's predictions in a quantifiable manner. We show that this statistic can easily distinguish between different models in cases where the `chi^2' statistic fails. We also show that the last mode of Crossing Statistic is identical to `chi^2', so that one can consider it as a generalization of `chi^2'. It is applicable to a variety of circumstances, although we consider it to be especially well suited to the task of distinguishing between different cosmological models using type Ia supernovae.

This talk can be useful for all physicists (or people from any other field of science) dealing with data, model selection and parameter estimation.